Tropic Marin Precision Hydrometrer Corrections - Redux

[Randy Holmes-Farley]

Yeah, definitely a complicated process if you want to account for ALL the variables. Best of luck!

IMO, it’s desirable that someone know the details. How else can one have confidence?

 

[BeanAnimal]

That part is certainly useful! I'll start a thread at BRS to see what can be done.

I just searched for it and can’t seem to find it now either. I am traveling this afternoon but will check the bookmarks when I get back. I just looked recently when I started compiling this data.

 

[Reefahholic]

IMO, it’s desirable that someone know the details. How else can one have confidence?

You and Beananimal are the perfect two reefers to figure out all the different variables for the glass material, thermal expansion, meniscus behavior, liquid viscosity, etc. I’ll be interested to see what you guys come up with.

Following….

 

[BeanAnimal]

updates - I absolutely am unable to find the BRS table on their site. It does look like it has been removed. I did not bother with the wayback machine. So that is good. I also can't find the BRS video or two that it was linked in.

I finished the calculator as a learning experience and as a practical exercise and tool.

Tropic Marin Precision Hydrometer Correction Calculator | BeanAnimal's Reef

Use this simple calculator to temperature correct your Tropic Marin Precision Floating Hydrometer readings and never guess about your aquarium salinity again!

beananimal.com

It outputs both the direct lookup (interpolated for values not actually in the table) form the table and also the values as calculated by the accepted UNESCO and PSS-78 equations.

I did not add an option for other hydrometers... as in my search I really found none as suitable as the Tropic Marin. Most are 0.001 Sg and the TM is 0.0001

Here is my takeaway - Either the empirical table or the direct calculation will work just fine. So my calculator, Hamzas, etc. all use the same accepted equations and the output matches the table in Randy's article close enough to not matter. There are some outlier spots where the table deviates a bit and the resultant PSU is .5 to 1.0 apart (empirical vs calculated) but they are rare.

I was going to had correct the oddball spots in the table, but decided to leave it as-is and just present both the lookup value and the calculated value.

I am not an expert in this field, but am happy to try to answer questions. That said I think Randy's article covers it well enough to begin with.

Ohh and in trying to wrap my head around this mess.. I banged out a Smolov Jr. calculator too (something easier on the mind as far as logic). If you know what it is... great, if not that is fine too.

 

[taricha]

erm... I played with it a bit and am now confused

Why does your "calculated" which I think should just be from the equations of state relationship (ignoring the hydrometer) differ from this calculator that claims also to be doing the same thing....
https://reefapp.net/en/salinity-calculator

On your calculator, water that was 35.0 PSU & 1.0264 at 25C would be 1.0257 SG at 28C.

on the reefapp calculator, the water temp correction is super tiny. 1.0264/ 35.0 PSU at 25C is given as 1.0263 at 28C.

I don't know what the actual "equations of state" relationship should be here. So I don't know whose implementation is right, but I expected those to be the same?

 

[BeanAnimal]

it looks like ReefApp is more of a simple unit converter, directly converting specific gravity (SG) to salinity (PSU) and vice versa, assuming the input is already accurate for the temperature you're measuring at. So, if you enter 1.0264 at 28°C, it assumes that's a correct reading at 28°C without needing further temperature adjustment. I have no clue what the 25C column is doing, but I think it is simply working the same conversion input with a 25C device at that input.

On the other hand, my calculator compensates for the input temperature, adjusting the reading back to the reference temperature (usually 25°C). So in other words, the density is compensated for between the actual and the reference and THEN the unit conversion is done.

I hope that makes sense.

 

[taricha]

Had been thinking about this thread a bit off and on.
One of the the things that makes following the logic of the conversions confusing is that a floating hydrometer is fundamentally a density device, but we mark it in SG.
What I mean is that the underlying physics is that the fraction submerged of a floating object is the ratio of density of the object to the density of the fluid. Each marking on a floating hydrometer is therefore a certain density ratio between the hydrometer and fluid. (ignoring meniscus force effects etc) But we don't mark it in density, we mark it in S.G. so we need a big fat table of corrections.

Using volumetric flask + scale with temp matched distilled water and saltwater, is fundamentally measuring S.G. - the ratio of mass to mass of equal volumes (and thus density to density ratio).

I also realized I don't know what a swing arm hydrometer is doing in terms of underlying physics. Why would a plastic arm in a certain density fluid float at a fixed angle around a pivot point? I'm gonna have to figure that out, because it's annoying.

 

[taricha]

File this under pretty-detailed-answers-to-questions-nobody-was-asking ....

I also realized I don't know what a swing arm hydrometer is doing in terms of underlying physics. Why would a plastic arm in a certain density fluid float at a fixed angle around a pivot point? I'm gonna have to figure that out, because it's annoying.

The swing arm is made of two different materials, plastic arm with an inset of a denser material. The denser material allows you to have the center of volume for the swing arm in a different place than the center of mass. This is helpful because the upward buoyant force acts at the center of volume, while the downward force of gravity acts on the center of mass.

At first I thought that this alone might let the swing arm reach equilibrium at a different angle for different buoyant force (different fluid density), but it doesn't...

left pic: The swing arm with a denser inset (grey circle) along the center of the arm.
You work out the condition for balanced torques, and the angle dependence goes away, so it fails. You don't get a different angle for different buoyant force.

It turns out you have to put the denser inset off-center on the swing arm, then the physics works.

left pic: denser inset (grey circle) off-center on the swing arm puts the center of volume and the center of mass at different angles. This means the torques exerted by the buoyant force and the force of gravity act at different angles. And if you work out the details, you get that changing the buoyant force (different fluid density) changes the angle ratio.

Just to be sure we have the right direction of effect, here's some made-up angle numbers applied to that last relationship on the bottom right. Let's pretend that the denser inset causes the center of mass to be 5 degrees angle below the center of volume.
cos(40)/cos(45) = 1.083
cos(30)/cos(35) = 1.057
cos(20)/cos(25) = 1.037

(those aren't density numbers, btw)

So the made up numbers agree with experience that a higher density fluid (greater buoyant force) causes the swing arm to reach a higher equilibrium angle.
And that a difference of a few % in buoyant force can cause big swings of angle in the arm, which is what you see when you use them.

And that's how the denser inset being off center toward the bottom of the swing arm gives you the angle dependence on fluid density.

 

[taricha]

BTW, this doesn't answer how a swing arm is mostly temperature independent. I'll have to think about that one some more.

 

[Randy Holmes-Farley]

BTW, this doesn't answer how a swing arm is mostly temperature independent. I'll have to think about that one some more.

I think it is because the materials expand with a similar expansion with temp as water, unlike glass which is much lower. That’s what I’ve always assumed, anyway.

Thanks for the interesting analysis!

 

[BeanAnimal]

I started to answer yesterday - then mentally came to the conclusion that my answer was going to be incorrect as I could not account for different densities reading different angles without some other sort of voodoo...

Thank you for taking the time to do the research and post the voodoo!

I think it is because the materials expand with a similar expansion with temp as water, unlike glass which is much lower. That’s what I’ve always assumed, anyway.

Thanks for the interesting analysis!

I would imagine that they are more temperature dependent than generally assumed. The density of the liquid is changing. I suppose we could ask taricha to add a layer of math and do some testing

 

[taricha]

I would imagine that they are more temperature dependent than generally assumed. The density of the liquid is changing. I suppose we could ask taricha to add a layer of math and do some testing

Randy's right, I think. If you want a device like this to be temperature independent, the swing arm needs to have the same temp expansion coefficient as water.
if we look at the last equation...


for the angle dependence on the right to stay the same while we increase the temp, we need the expression on the left to stay the same. The length ratio won't change, and the weight of the swing arm, Fg won't change. So to be perfectly temp-invariant, we need the buoyant force, Fb to stay the same.

Buoyant force is weight of displaced water, and as water gets warmer, it expands. So a fixed volume would displace a smaller mass of water, so the volume of the swing arm needs to increase by the same amount as the volume of the water increase. If the plastic arm increased volume per degree temp increase the same as water, then it would displace an increasing volume to exactly match the increasing volume of a set amount of water, and thus the buoyant force would be the same and the equilibrium angle would be unchanged with temp increase.

experimentally, how well this actually worked depends on how closely your plastic arm actually matched the expansion coefficient of water. My Instant Ocean hydrometer could be good or bad. Never tried changing the temp to look for how well it corrects.

 

[Randy Holmes-Farley]

experimentally, how well this actually worked depends on how closely your plastic arm actually matched the expansion coefficient of water. My Instant Ocean hydrometer could be good or bad. Never tried changing the temp to look for how well it corrects.

When I tested two swing arms years ago, the temp correction was quite good even if the absolute values were off:

So how do these hydrometers measure up? In my tank the water was measured to be S=35 ± 0.5 by conductivity. Using the Deep Six swing arm hydrometer I got readings of S=32.5 ± 0.5 at 81 °F and S=32 ± 0.5 at 68 °F. Using the SeaTest I got S=34.5 ± 0.5 at 81 °F and S=34 ± 0.5 at 68 °F.

For the standard type Tropic Marin hydrometer, I got a 77 °F/77 °F specific gravity of about 1.0265 ± 0.0003 (Figure 4), which compares well to the expected value of 1.0264.

Chemistry and the Aquarium: Specific Gravity: Oh How Complicated!

This month, Randy explains and reviews specific gravity.

reefs.com

 

[taricha]

Here's my Instant Ocean swing arm hydrometer temp performance. Essentially unchanged - within expected precision for that device over the entire likely temp range of tank water.